The Itô integral with respect to an infinite dimensional Lévy process: A series approach

Abstract

We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes. We also prove that this stochastic integral coincides with the Itô integral that has been developed in the literature.

21 pages

References in corpus (4)

• Stochastic integration in UMD Banach spaces
• Existence of Lévy term structure models
• Isomorphisms for spaces of predictable processes and an extension of the Itô integral
• A note on stochastic integrals as $L^2$-curves